Probability of getting a hand with at least 6 doubles in domino

Mathematics Asked by Rolando González on December 21, 2020

I have this problem:

Domino has 28 tiles with 7 doubles. Each hand has 7 tiles. What is the probability of getting a hand with at least 6 doubles?

Since it’s an "at least" kind of problem I did the following:

Total number of hands: $$28C7$$

$$P(hand with at least 6 doubles) = 1 – P(no double ) – P(one double )- P(two doubles )-dots – P(six doubles ) = 1- bigg( frac{(7C0 times 21C7)+ (7C1 times 21C6) + (7C2 times 21C5) + (7C3 times 21C4) + (7C4 times 21C3) + (7C5 times 21C1) + (7C6 times 21C1) }{28C7} bigg)$$

This gives me a probability of $$0.8035$$ but I’m doubtful if my approach was correct. Is it right or is there another way of solving this?

Thanks.

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